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  • July 2014

Optics InfoBase > Spotlight on Optics > Inverse analysis of the rainbow for the case of low-coherent incident light to determine the diameter of a glass fiber


Inverse analysis of the rainbow for the case of low-coherent incident light to determine the diameter of a glass fiber

Published in Applied Optics, Vol. 53 Issue 19, pp.4239-4247 (2014)
by Grzegorz Świrniak, Grzegorz Głomb, and Janusz Mroczka

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Spotlight summary: Optical techniques are routinely used for high-precision non-contact gauging. At micron to millimeter scales, microscopy is perhaps the most intuitive and widely-used technique. However, a variety of non-imaging techniques are also available - interferometry, for example, offers sub-wavelength precision at the expense of increased instrument complexity. Fundamentally, all non-contact optical metrology techniques rely on a contrast mechanism (so that the measured object affects an optical field) and the solution of an inverse problem (allowing data interpretation by relating the optical field back to the properties of interest in the object). In some cases the inverse problem may be trivial, and in others only a qualitative understanding of the contrast mechanism is necessary to extract the desired information. In this paper Swirniak, Glomb and Mroczka discuss a technique where a precise quantitative understanding of the contrast mechanism is in fact necessary, and the inverse problem is decidedly non-trivial. The authors describe how measurement implementation choices can be made specifically to simplify the inverse problem, mitigating effects that would otherwise render data interpretation impractical.

The task considered is to measure the diameter of a cylindrical fiber by examining the angular profile of light scattered from the fiber. For this problem, the contrast mechanism (or forward model) is rigorously understood and is described by Lorenz-Mie theory. However, the inverse problem is complicated by phenomena that vary significantly and non-linearly with the fiber geometry. For example, with monochromatic illumination the angular dependence of the signal can vary rapidly with observation angle, and in a way that may change significantly with very small changes in fiber diameter. So while scattering from the fiber can be accurately modeled as a function of diameter, in certain diameter ranges recovering the fiber size is impractical in the presence of noise and small experimental uncertainties. Here the authors show that the stability of the inverse problem can be improved by using an illumination source with a broader spectral profile. Doing so results in many of the contrast sensitivities averaging out, and means that the system can be modeled with the simpler Airy’s theory of rainbows (albeit augmented with a correction) rather than the full Lorenz-Mie solution. This provides a computational simplification but, more importantly, reduces the detrimental sensitivity of the data to small changes in fiber properties. This is shown to allow high precision diameter estimates which, interestingly, are robust even to some un-modeled refractive index variations within the fiber. By exploring the physical relationship between the data collection instrumentation and the inverse problem, the authors have shown a clear route to improving the measurement process.

--Brynmor Davis



Technical Division: Light–Matter Interactions
ToC Category: Scattering
OCIS Codes: (060.2270) Fiber optics and optical communications : Fiber characterization
(290.3200) Scattering : Inverse scattering
(290.5850) Scattering : Scattering, particles


Posted on July 29, 2014

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